Measuring the impact of an environmental point source exposure on the risk of disease, like cancer or childhood asthma, is well-developed. Modeling how an environmental health hazard that is extensive in space, like a wastewater canal, is not. We propose a novel Bayesian generative semiparametric model for characterizing the cumulative spatial exposure to an environmental health hazard that is not well-represented by a single point in space. The model couples a dose-response model with a log-Gaussian Cox process integrated against a distance kernel with an unknown length-scale. We show that this model is a well-defined Bayesian inverse model, namely that the posterior exists under a Gaussian process prior for the log-intensity of exposure, and that a simple integral approximation adequately controls the computational error. We quantify the finite-sample properties and the computational tractability of the discretization scheme in a simulation study. Finally, we apply the model to survey data on household risk of childhood diarrheal illness from exposure to a system of wastewater canals in Mezquital Valley, Mexico.

翻译：测量点源暴露对疾病风险（如癌症或儿童哮喘）的影响已有较为成熟的方法。然而，针对空间广布的环境健康危害（如污水渠）的暴露建模尚不完善。本文提出一种新颖的贝叶斯生成半参数模型，用于刻画空间上难以用单一点表征的环境健康危害的累积空间暴露。该模型将剂量-反应模型与具有未知长度尺度的距离核积分结合的对数高斯Cox过程耦合。我们证明该模型是一个定义良好的贝叶斯逆模型，即在高斯过程先验假设下暴露对数强度的后验分布存在，且简单积分近似能充分控制计算误差。通过模拟研究，我们量化了离散化方案的有限样本性质及计算可行性。最后，我们将该模型应用于墨西哥梅斯基塔尔山谷污水渠系统暴露导致的家庭儿童腹泻疾病风险调查数据。